A Crank-Nicolson Difference Scheme for Solving a Type of Variable Coefficient Delay Partial Differential Equations

A linearized Crank-Nicolson difference scheme is constructed to solve a type of variable coefficient delay partial differential equations. The difference scheme is proved to be unconditionally stable and convergent, where the convergence order is two in both space and time. A numerical test is provided to illustrate the theoretical results

A Compact Difference Scheme for a Class of Variable Coefficient Quasilinear Parabolic Equations with Delay

A linearized compact difference scheme is provided for a class of variable coefficient parabolic systems with delay. The unique solvability, unconditional stability, and convergence of the difference scheme are proved, where the convergence order is four in space and two in time. A numerical test is presented to illustrate the theoretical results